A right angle triangle has ∠AOB =90°, AC = BC, OA = 12 cm and OC = 6.5 and OB is its base. Find the measure of OB.

We have

Given: ∆AOB is a right-angled triangle, right angled at O.

AC = BC

⇒ C is the mid-point of AB.

OA = 12 cm

OC = 6.5 cm

Now the mid-point of the hypotenuse of a right triangle is equidistant from the vertices.

Therefore, AC = BC = OC

⇒ AC = BC = 6.5 cm [∵ OC = 6.5cm]

Now, AB = AC + BC [∵ C is the midpoint of AB]

⇒ AB = 6.5 + 6.5

⇒ AB = 13 cm

According to Pythagoras theorem in ∆AOB,

AO² + OB² = AB²

⇒ OB² = AB² - AO²

⇒ OB² = 13² - 12²

⇒ OB² = 169 - 144

⇒ OB² = 25

⇒ OB = √25 = 5 cm

Thus, OB = 5 cm.